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Systems Analysis and Control

Systems Analysis and ControlMatthew M. PeetArizona State UniversityLecture 21: Stability Margins and Closing the LoopOverviewIn this Lecture, you will learn:Closing the Loop Effect on Bode plot Effect on StabilityStability Effects Gain Margin Phase Margin BandwidthEstimating Closed-Loop Performance using Open-Loop Data Damping Ratio Settling Time Rise TimeM. PeetLecture 21: Control Systems2 / 31 ReviewRecall: Frequency ResponseInput:u(t) =Msin( t+ )Output:Magnitude and Phase Shifty(t) =|G( )|Msin( t+ + G( ))02468101214161820 2 1 Simulation ResultsTime (sec)AmplitudeFrequency Response tosin tis given byG( )M.

Review Recall:Bode Plot De nition 1. The Bode Plot is a pair of log-log and semi-log plots: 1.Magnitude Plot: 20log 10 jG({!)jvs. log 10! 2.Phase Plot: \G({!) vs. log 10! Bite-Size Chucks: \G({!) = X i \G i({!) M. Peet Lecture 21: Control Systems 4 / 31

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